报告题目：Fiber Orientation Distribution Estimation Using a Peaceman Rachford Splitting Method

报告人：戴彧虹研究员  中国科学院数学与系统科学研究院

时  间：2016年12月1日    上午10:15-11:00

地  点：东区管理科研楼  数学科学学院1218

内容提要：

In diffusion-weighted magnetic resonance imaging, the estimation of the orientations of multiple nerve fibers in each voxel (the fiber orientation distribution (FOD)) is a critical issue for exploring the connection of cerebral tissue. In this paper, we establish a convex semidefinite programming (CSDP) model for the FOD estimation. One feature of the new model is that it can ensure the statistical meaning of FOD since as a probability density function, FOD must be nonnegative and have a unit mass. To construct such a statistically meaningful FOD, we consider its approximation by a sum of squares (SOS) polynomial and impose the unit-mass by a linear constraint. Another feature of the new model is that it introduces a new regularization based on the sparsity of nerve fibers. Due to the sparsity of the orientations of nerve fibers in cerebral white matter, a heuristic regularization is raised, which is inspired by the Z-eigenvalue of a symmetric tensor that closely relates to the SOS polynomial. To solve the CSDP efficiently, we propose a new Peaceman�Rachford splitting method and prove its global convergence. Numerical experiments on synthetic and real-world human brain data show that, when compared with some existing approaches for fiber estimations, the new method gives a sharp and smooth FOD. Further, the proposed Peaceman�Rachford splitting method is shown to have good numerical performances comparing several existing methods. This is a joint work with Yannan Chen and Deren Han.

报告人简介：

中国科学院数学与系统科学研究院冯康首席研究员戴彧虹教授，博士生导师，国家杰出青年基金获得者，中国运筹学会副理事长，数学规划分会理事长，中国科学院数学与系统科学研究院优化与应用中心副主任，剑桥大学博士后，曾荣获德国洪堡基金、钟家庆数学奖、冯康科学计算奖、第十届中国青年科技奖、国家自然科学奖二等奖。长期从事非线性优化、数值代数及其应用等方面的研究，已发表论文100多篇，主要代表性论文发表在Mathematical Programming 和IMA，SIAM，IEEE系列期刊上。